Constructing a unitary Hessenberg matrix from spectral data
By: William Gragg, Gregory Ammar, Lother Reichel
Contributors: Ammar, Gregory S.; Reichel, Lother; Naval Postgraduate School (U.S.). Dept. of Mathematics
Publisher: Naval Postgraduate School; Available from National Technical Information Service
Published: 1988
Place of publication: Monterey, Calif; Springfield, Va
Language: eng
Subjects: EIGENVALUES; NUMERICAL ANALYSIS; PERTURBATIONS; ALGORITHMS; SPECTRA
Other titles: NPS-53-89-005.
Description: We consider the numerical construction of a unitary Hessenberg matrix from spectral data using an inverse QR algorithm. Any unitary upper Hessenberg matrix H with nonnegative subdiagonal elements can be represented by 2n - 1 real parameters. This representation, which we refer to as the Schur parameterization of H, facilitates the development of efficient algorithms for this class of matrices. We show that a unitary upper Hessenberg matrix H with positive subdiagonal elements is determined by its eigenvalues and the eigenvalues of a rank-one unitary perturbation of H. The eigenvalues of the perturbation strictly interlace the eigenvalues of H on the unit circle. Inverse eigenvalue problem, Unitary matrix, Orthogonal polynomial.
Notes: Title from cover.

"NPS-53-89-005."

"November 1988."

AD A204 114.

Includes bibliographical references (p. 7)

aq/aq cc:9116 04/23/99.